I think some of the music from “The Ninth Gate” and “Star Wars Ep. 1: The Phantom Menace” would be appropriate.
On the pop side, there’s XTC’s “This World Over,” and their old concert-staple “Living Through Another Cuba”/“Generals and Majors” medley…
And of course, there’s always Tom Lehrer’s cheeky “We Will All Go Together (When We Go!),” which always cracks me up. 
Funny
The last day on Earth and NO ONE thinks of
“Its the End of the World as We know it” by REM
I figure by the time the world goes up, a moment of clarity and EVERYONE will know the lyrics to that song.
The Birthday Party! Nobody ever mentions The Birthday Party. They were great. My first copy having been destroyed I have recently been trying to find “(Sometimes) Pleasure Heads Must Burn” somewhere. Which, come to think of it, would be very appropriate for when the world ends and I shuffle off to my inevitable damnation.
But my first thought was Foetus. "Anything (Viva!) or maybe “Satan Place”.
Has anybody suggested “The Earth Dies Screaming” by Tom Waits yet?
I’d submit godspeed you black emperor!.
Either f#a# (infinity symbol) or Slow Riot for New Zero Kanada.
What Apocalypse would be complete without some Leonard Cohen? How about ‘The Future’?
*You don’t know me from the wind;
Ya never will, ya never did—
I’m the little Jew who wrote the Bible.
I’ve seen the Nations rise and fall.
I’ve heard their stories, heard them all
But love’s the only engine of survival.
Your servant here, he has been told
To say it clear, to say it cold:
“It’s over, it aint goin’ any further.”
And now the wheels of Heaven stop
You feel the Devil’s riding crop.
Get ready for the future;
It is murder.*
Bolt Thrower
“Cenotaph”
Heaviest song ever recorded, and certainly worthy of the end of the world.